When did Moshe, Aharon and his sons all wash from the Kiyor?
Rashi: On the eighth day of the Milu'im, when they all served as Kohanim in the Mishkan. 1
Moshav Zekenim (from Zevachim 19b): Even though they did not serve at once 2 , the verse teaches that the Kiyor must hold enough water for four Kohanim, corresponding to Moshe, Aharon and two sons. 3 In any case, Moshe needed to wash during the seven days of the Milu'in.
Riva (39:32): In Zevachim (19b), Rashi explained that they were not Kohanim at the same time; Moshe was Kohen the first seven days of the Milu'im, but not on the eighth. Tana'im argue about this.
Shitah Mekubetzes (19b): Since we include Moshe, even though he did not serve after Nisan 1, we should include also Nadav and Avihu, who served that day! Rather, the plural "u'Vanav" teaches only two. Ma'asei l'Melech (Hilchos Bi'as Mikdash 5:13) - Rashi here is like Rebbi (Zevachim 115b), who holds that Nadav and Avihu became Kohanim at Sinai; 'Banav' includes only them. Avi Ezri (ibid.) - it was already decreed that Nadav and Avihu die, so they are not counted. The Rambam there counts Aharon, Elazar and Isamar. His text of the Gemara said "Aharon u'Vanav" (30:19, the command to make the Kiyor), so he was forced to include Pinchas; this is like the opinion (Zevachim 101a) that Pinchas was already a Kohen.
Why must Kohanim wash their feet? They are not used for Avodah!
Moshav Zekenim citing R. Yeshayah; It is due to "Shemor Raglecha Ka'asher Telech El Beis ha'Elokim" (Koheles 4:17).